"Jeff is not a swimmer", symbolically I have to turn this into symbolic language:
 A: No swimmers are overweight
  B: Jeff is overweight
  Therefore, Jeff is not a swimmer

I got
$$A\to\neg B$$
$$B$$
$$\therefore\neg A$$
What do you think? Am I close?
Also I would say this is valid via universal modus tollens.
A: What you have is correct, where $A$ means "swimmer" and $B$ means "overweight".
One thing to point out: You translated "no swimmer is overweight" as $A \to \lnot B$. That is fine, but a more direct translation might be $\lnot (A \land B)$.
I would think of "$A \to \lnot B$" as "every swimmer is not overweight", and "$\lnot (A \land B)$" as "no swimmer is overweight." But of course the statements are logically equivalent, so it doesn't matter too much. Just pick the one you think is a more direct translation.
A: When the domain of discussion is implicitly about Jeff then, the modus tollens statement is okay.

$$\rm S\to\neg W, W \vdash \neg S$$
  
  
*
  
*If Jeff is a swimmer then Jeff is not overweight
  
*Jeff is overweight
  
*Therefore: Jeff is not a swimmer.
  

Otherwise, as suggested by @DanielV, you will need a predicate for being Jeff. 

$$\rm S\to\neg W, J\to W\, \vdash\, J\to\neg S$$
  
  
*
  
*If it is a swimmer, then it is not overweight.
  
*If it is Jeff, then it is overweight. 
  
*Therefore: If it is Jeff then it is not a swimmer.
  

This is equivalent to the Hypothetical Syllogism.  $\rm J\to W\,, W\to \neg S\, \vdash\, J\to\neg S$
